A Generalization of Nemhauser and Trotter's Local Optimization Theorem - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2009

A Generalization of Nemhauser and Trotter's Local Optimization Theorem

Michael R. Fellows
  • Function : Author
  • PersonId : 857972
Jiong Guo
  • Function : Author
  • PersonId : 857973
Hannes Moser
  • Function : Author
  • PersonId : 857974
Rolf Niedermeier
  • Function : Author
  • PersonId : 857975


The Nemhauser-Trotter local optimization theorem applies to the NP-hard Vertex Cover problem and has applications in approximation as well as parameterized algorithmics. We present a framework that generalizes Nemhauser and Trotter's result to vertex deletion and graph packing problems, introducing novel algorithmic strategies based on purely combinatorial arguments (not referring to linear programming as the Nemhauser-Trotter result originally did). We exhibit our framework using a generalization of Vertex Cover, called Bounded- Degree Deletion, that has promise to become an important tool in the analysis of gene and other biological networks. For some fixed d ≥ 0, Bounded-Degree Deletion asks to delete as few vertices as possible from a graph in order to transform it into a graph with maximum vertex degree at most d. Vertex Cover is the special case of d = 0. Our generalization of the Nemhauser-Trotter theorem implies that Bounded-Degree Deletion has a problem kernel with a linear number of vertices for every constant d. We also outline an application of our extremal combinatorial approach to the problem of packing stars with a bounded number of leaves. Finally, charting the border between (parameterized) tractability and intractability for Bounded-Degree Deletion, we provide a W[2]-hardness result for Bounded-Degree Deletion in case of unbounded d-values.
Fichier principal
Vignette du fichier
fellows_new.pdf (253.1 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

inria-00360058 , version 1 (10-02-2009)


  • HAL Id : inria-00360058 , version 1
  • ARXIV : 0902.2149


Michael R. Fellows, Jiong Guo, Hannes Moser, Rolf Niedermeier. A Generalization of Nemhauser and Trotter's Local Optimization Theorem. 26th International Symposium on Theoretical Aspects of Computer Science STACS 2009, Feb 2009, Freiburg, Germany. pp.409-420. ⟨inria-00360058⟩


44 View
375 Download



Gmail Facebook Twitter LinkedIn More